Multi-objective optimization for planning liner shipping service with uncertain port times

This paper considers a joint tactical planning problem for the number of ships, the planned maximum sailing speed, and the liner service schedule in order to simultaneously optimize the expected cost, the service reliability and the shipping emission in the presence of port time uncertainty. The problem is formulated into a stochastic multi-objective optimization problem at the operational level. The relationships between the objectives and the decision variables are established. A simulation-based non-dominated sorting genetic algorithm is then presented to solve this problem. A case study is provided to illustrate the results and the application of the model.